TSTP Solution File: NUM386+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM386+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n024.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 10:37:10 EDT 2023

% Result   : Theorem 0.60s 0.63s
% Output   : CNFRefutation 0.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   31
% Syntax   : Number of formulae    :   58 (   8 unt;  27 typ;   0 def)
%            Number of atoms       :  101 (  38 equ)
%            Maximal formula atoms :   20 (   3 avg)
%            Number of connectives :  115 (  45   ~;  54   |;  10   &)
%                                         (   6 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   20 (  14   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :   19 (  19 usr;  13 con; 0-3 aty)
%            Number of variables   :   58 (   4 sgn;  27   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    in: ( $i * $i ) > $o ).

tff(decl_23,type,
    empty: $i > $o ).

tff(decl_24,type,
    function: $i > $o ).

tff(decl_25,type,
    relation: $i > $o ).

tff(decl_26,type,
    one_to_one: $i > $o ).

tff(decl_27,type,
    set_union2: ( $i * $i ) > $i ).

tff(decl_28,type,
    succ: $i > $i ).

tff(decl_29,type,
    singleton: $i > $i ).

tff(decl_30,type,
    element: ( $i * $i ) > $o ).

tff(decl_31,type,
    empty_set: $i ).

tff(decl_32,type,
    relation_empty_yielding: $i > $o ).

tff(decl_33,type,
    relation_non_empty: $i > $o ).

tff(decl_34,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_35,type,
    esk2_3: ( $i * $i * $i ) > $i ).

tff(decl_36,type,
    esk3_1: $i > $i ).

tff(decl_37,type,
    esk4_0: $i ).

tff(decl_38,type,
    esk5_0: $i ).

tff(decl_39,type,
    esk6_0: $i ).

tff(decl_40,type,
    esk7_0: $i ).

tff(decl_41,type,
    esk8_0: $i ).

tff(decl_42,type,
    esk9_0: $i ).

tff(decl_43,type,
    esk10_0: $i ).

tff(decl_44,type,
    esk11_0: $i ).

tff(decl_45,type,
    esk12_0: $i ).

tff(decl_46,type,
    esk13_0: $i ).

tff(decl_47,type,
    esk14_0: $i ).

tff(decl_48,type,
    esk15_0: $i ).

fof(t13_ordinal1,conjecture,
    ! [X1,X2] :
      ( in(X1,succ(X2))
    <=> ( in(X1,X2)
        | X1 = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_ordinal1) ).

fof(d1_ordinal1,axiom,
    ! [X1] : succ(X1) = set_union2(X1,singleton(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_ordinal1) ).

fof(d2_xboole_0,axiom,
    ! [X1,X2,X3] :
      ( X3 = set_union2(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,X1)
            | in(X4,X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).

fof(d1_tarski,axiom,
    ! [X1,X2] :
      ( X2 = singleton(X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> X3 = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).

fof(c_0_4,negated_conjecture,
    ~ ! [X1,X2] :
        ( in(X1,succ(X2))
      <=> ( in(X1,X2)
          | X1 = X2 ) ),
    inference(assume_negation,[status(cth)],[t13_ordinal1]) ).

fof(c_0_5,negated_conjecture,
    ( ( ~ in(esk14_0,esk15_0)
      | ~ in(esk14_0,succ(esk15_0)) )
    & ( esk14_0 != esk15_0
      | ~ in(esk14_0,succ(esk15_0)) )
    & ( in(esk14_0,succ(esk15_0))
      | in(esk14_0,esk15_0)
      | esk14_0 = esk15_0 ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).

fof(c_0_6,plain,
    ! [X12] : succ(X12) = set_union2(X12,singleton(X12)),
    inference(variable_rename,[status(thm)],[d1_ordinal1]) ).

fof(c_0_7,plain,
    ! [X20,X21,X22,X23,X24,X25,X26,X27] :
      ( ( ~ in(X23,X22)
        | in(X23,X20)
        | in(X23,X21)
        | X22 != set_union2(X20,X21) )
      & ( ~ in(X24,X20)
        | in(X24,X22)
        | X22 != set_union2(X20,X21) )
      & ( ~ in(X24,X21)
        | in(X24,X22)
        | X22 != set_union2(X20,X21) )
      & ( ~ in(esk2_3(X25,X26,X27),X25)
        | ~ in(esk2_3(X25,X26,X27),X27)
        | X27 = set_union2(X25,X26) )
      & ( ~ in(esk2_3(X25,X26,X27),X26)
        | ~ in(esk2_3(X25,X26,X27),X27)
        | X27 = set_union2(X25,X26) )
      & ( in(esk2_3(X25,X26,X27),X27)
        | in(esk2_3(X25,X26,X27),X25)
        | in(esk2_3(X25,X26,X27),X26)
        | X27 = set_union2(X25,X26) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_xboole_0])])])])])]) ).

cnf(c_0_8,negated_conjecture,
    ( ~ in(esk14_0,esk15_0)
    | ~ in(esk14_0,succ(esk15_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,plain,
    succ(X1) = set_union2(X1,singleton(X1)),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,plain,
    ( in(X1,X3)
    | ~ in(X1,X2)
    | X3 != set_union2(X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_11,plain,
    ! [X13,X14,X15,X16,X17,X18] :
      ( ( ~ in(X15,X14)
        | X15 = X13
        | X14 != singleton(X13) )
      & ( X16 != X13
        | in(X16,X14)
        | X14 != singleton(X13) )
      & ( ~ in(esk1_2(X17,X18),X18)
        | esk1_2(X17,X18) != X17
        | X18 = singleton(X17) )
      & ( in(esk1_2(X17,X18),X18)
        | esk1_2(X17,X18) = X17
        | X18 = singleton(X17) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_tarski])])])])])]) ).

cnf(c_0_12,negated_conjecture,
    ( in(esk14_0,succ(esk15_0))
    | in(esk14_0,esk15_0)
    | esk14_0 = esk15_0 ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_13,negated_conjecture,
    ( ~ in(esk14_0,esk15_0)
    | ~ in(esk14_0,set_union2(esk15_0,singleton(esk15_0))) ),
    inference(rw,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_14,plain,
    ( in(X1,set_union2(X2,X3))
    | ~ in(X1,X2) ),
    inference(er,[status(thm)],[c_0_10]) ).

cnf(c_0_15,negated_conjecture,
    ( esk14_0 != esk15_0
    | ~ in(esk14_0,succ(esk15_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_16,plain,
    ( in(X1,X3)
    | ~ in(X1,X2)
    | X3 != set_union2(X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_17,plain,
    ( X1 = X3
    | ~ in(X1,X2)
    | X2 != singleton(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_18,plain,
    ( in(X1,X3)
    | in(X1,X4)
    | ~ in(X1,X2)
    | X2 != set_union2(X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_19,negated_conjecture,
    ( esk15_0 = esk14_0
    | in(esk14_0,esk15_0)
    | in(esk14_0,set_union2(esk15_0,singleton(esk15_0))) ),
    inference(rw,[status(thm)],[c_0_12,c_0_9]) ).

cnf(c_0_20,negated_conjecture,
    ~ in(esk14_0,esk15_0),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_21,negated_conjecture,
    ( esk15_0 != esk14_0
    | ~ in(esk14_0,set_union2(esk15_0,singleton(esk15_0))) ),
    inference(rw,[status(thm)],[c_0_15,c_0_9]) ).

cnf(c_0_22,plain,
    ( in(X1,set_union2(X2,X3))
    | ~ in(X1,X3) ),
    inference(er,[status(thm)],[c_0_16]) ).

cnf(c_0_23,plain,
    ( X1 = X2
    | ~ in(X1,singleton(X2)) ),
    inference(er,[status(thm)],[c_0_17]) ).

cnf(c_0_24,plain,
    ( in(X1,X2)
    | in(X1,X3)
    | ~ in(X1,set_union2(X3,X2)) ),
    inference(er,[status(thm)],[c_0_18]) ).

cnf(c_0_25,negated_conjecture,
    ( esk14_0 = esk15_0
    | in(esk14_0,set_union2(esk15_0,singleton(esk15_0))) ),
    inference(sr,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_26,negated_conjecture,
    ~ in(esk14_0,singleton(esk15_0)),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).

cnf(c_0_27,plain,
    ( in(X1,X3)
    | X1 != X2
    | X3 != singleton(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_28,negated_conjecture,
    esk14_0 = esk15_0,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_20]),c_0_26]) ).

cnf(c_0_29,plain,
    in(X1,singleton(X1)),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_27])]) ).

cnf(c_0_30,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_28]),c_0_29])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : NUM386+1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34  % Computer : n024.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Fri Aug 25 15:10:39 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.20/0.61  start to proof: theBenchmark
% 0.60/0.63  % Version  : CSE_E---1.5
% 0.60/0.63  % Problem  : theBenchmark.p
% 0.60/0.63  % Proof found
% 0.60/0.63  % SZS status Theorem for theBenchmark.p
% 0.60/0.63  % SZS output start Proof
% See solution above
% 0.60/0.64  % Total time : 0.013000 s
% 0.60/0.64  % SZS output end Proof
% 0.60/0.64  % Total time : 0.016000 s
%------------------------------------------------------------------------------